Each character can only use the weapons/armor available to it as shown on the equipment list towards the front of the warband rules. For instance, if you look at the skaven equipment list, there's a hero list and a henchman list. The hero list only has three armor entries: light armor, buckler, and helmet. Thus any model which uses the skaven heroes list can never use any other armor. Shields and heavy armor cannot be used. That is the armor restriction.
Note that ithilmar and gromril armor are just special types of heavy armor. Anyone who can wear heavy armor can wear ithilmar or gromril armor; they do not need to be listed in the equipment list.
Certain warbands such as skaven do not have access to all types of armor (in this case, light armor).